Quadratic functions are second-order equations of the form y=ax^2+bx+c. Their graphs form parabolas. The defining characteristic of a quadratic is that the acceleration of the outputs is a constant.
Answer:
a = -9
Step-by-step explanation:
8 - a = 17
8 -17 = a
-9 = a
Answer:
The greatest number of people that can attend the meeting on that budget is 116
Step-by-step explanation:
The cost for the meeting is given by the following expression:
cost = 500 + 6*person
Since the budget is $1200 the cost must be at most equal to that, therefore:
1200 = 500 + 6*person
500 + 6*person = 1200
6*person = 1200 - 500
6*person = 700
person = 700/6 = 116.667
Since there can't be a 0.667 person, the greatest number of people that can attend the meeting on that budget is 116
It sounds like everything is being described in reference to angle A, so a good starting point is to pick a variable to represent the measure of angle A. I'm going to use "a" for that.
Next, I'm going to take the verbal descriptions in the problem and "translate" them into "math language". They say angle B is 5 times angle A, so that means the measure of angle B is actually 5a. The size of angle C is 5 degrees less than 4 times the size of A, so that translates to 4a-5.
We now know the following:
Angle A: a
Angle B: 5a
Angle C: 4a-5
Now, to find the value of a, we need to remember that all the angles in a triangle add up to 180 degrees.
So we have: a+5a+4a-5 = 180
We can solve that equation by combining like terms to get: 10a-5=180
We can add 5 to both sides: 10a =185
And divide by 10: a = 18.5
That tells us the measure of angle A! (It's 18.5 degrees). Now we can go back and find B by multiplying A by 5. We get 92.5 degrees for that.
Finally, we can find C by taking 4*18.5-5. We get 69 degrees for that.
One last thing-- let's check that they really do add up to 180! 69+92.5+18.5 = 180. Yep!
Hope that helps you!!
Answer:
60
Step-by-step explanation:
The shaded region's area is the difference between the area of the outer rectangle and the white rectangle.
area = LW - lw
area = (4 + 4)(9 + 3) - (4)(9)
area = (8)(12) - 36
area = 96 - 36
area = 60
